I'd still recommend a separate server for numerous reasons:
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You can save power instead of letting your gaming PC run 24/7. The lowest I've ever seen my gaming PC idle at is 125W, whereas my dedicated DIY NAS idles at 27W. That's a huge difference in your electricity bill over the long-term, although it really depends on what area you live in. My PC kicks out a lot more heat than my server though so it does make a difference when it comes to my AC bill!
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You may want stable software for your server (ie Debian) and bleeding edge (Arch Linux) for your gaming PC, or you may want Linux for your server and Windows for gaming, etc.
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Separate server provides better uptime. I would hate to interrupt a big transfer to my Nextcloud just because I needed to restart my PC to do system updates.